arxiv:2307.01463

Hybrid two-level MCMC for Bayesian Inverse Problems

Published on Jul 4, 2023

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Abstract

A hybrid two-level MCMC method combines AI surrogate models and numerical models to solve Bayesian inverse problems efficiently and accurately with minimal numerical samples.

AI-generated summary

We introduced a novel method to solve Bayesian inverse problems governed by PDE equations with a hybrid two-level MCMC where we took advantage of the AI surrogate model speed and the accuracy of numerical models. We show theoretically the potential to solve Bayesian inverse problems accurately with only a small number of numerical samples when the AI surrogate model error is small. Several numerical experiment results are included which demonstrates the advantage of the hybrid method.

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